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## Homework Statement

The net force on the mass is the central force F(r) = -k(r-a). Find the potential energy U(r).

a is the spring of natural length and k is spring constant k.

## Homework Equations

-dU/dx = F(x)

## The Attempt at a Solution

[tex]F(r) = - \frac{ dU }{ dr } implies -k(r-a) = - \frac{ dU }{ dr }[/tex]

So I did this and then integrating both sides I got

[tex]\frac{ kr^2 }{ 2} - kar = U(r)[/tex] but this doesn't make much sense when I graph it out, as it gives me a parabola, and I would be expecting a asymptotic type function?